IEEE Trans Image Process - Efficient variational Bayesian approximation method based on subspace optimization.

Tópicos

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Resumo

Variational Bayesian approximations have been widely used in fully Bayesian inference for approximating an intractable posterior distribution by a separable one. Nevertheless, the classical variational Bayesian approximation (VBA) method suffers from slow convergence to the approximate solution when tackling large dimensional problems. To address this problem, we propose in this paper a more efficient VBA method. Actually, variational Bayesian issue can be seen as a functional optimization problem. The proposed method is based on the adaptation of subspace optimization methods in Hilbert spaces to the involved function space, in order to solve this optimization problem in an iterative way. The aim is to determine an optimal direction at each iteration in order to get a more efficient method. We highlight the efficiency of our new VBA method and demonstrate its application to image processing by considering an ill-posed linear inverse problem using a total variation prior. Comparisons with state of the art variational Bayesian methods through a numerical example show a notable improvement in computation time.

Resumo Limpo

variat bayesian approxim wide use fulli bayesian infer approxim intract posterior distribut separ one nevertheless classic variat bayesian approxim vba method suffer slow converg approxim solut tackl larg dimension problem address problem propos paper effici vba method actual variat bayesian issu can seen function optim problem propos method base adapt subspac optim method hilbert space involv function space order solv optim problem iter way aim determin optim direct iter order get effici method highlight effici new vba method demonstr applic imag process consid illpos linear invers problem use total variat prior comparison state art variat bayesian method numer exampl show notabl improv comput time

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